Meshfree numerical simulation of free surface thermal flows in mould filling processes using the Finite Pointset Method

The purpose of this work is to carry out a meshfree implementation for the numerical simulation of two-dimensional transient incompressible free surface flows coupled with heat transfer. The Finite Pointset Method is applied in order to solve the involved partial differential equations where the corresponding classical or strong formulation is directly used instead of the corresponding weak form as needed for some other meshfree approaches. The incorporation of the boundary conditions is done in a direct and simple manner. The simplicity and efficiency of this numerical method are demonstrated on two complex two-dimensional mould filling processes.